We discuss the source of the apparent ambiguities arising in the calculation of the dynamics of binary black holes within the post-Newtonian framework. Divergences appear in both the near and far zone calculations, and may be of either ultraviolet (UV) or infrared (IR) nature. The effective field theory (EFT) formalism elucidates the origin of the singularities which may introduce apparent ambiguities. In particular, the only (physical) “ambiguity parameters” that necessitate a matching calculation correspond to unknown finite size effects, which first appear at fifth post-Newtonian (5PN) order for nonspinning bodies. We demonstrate that the ambiguities linked to IR divergences in the near zone, that plague the recent derivations of the binding energy at 4PN order, both in the Arnowitt, Deser, and Misner (ADM) and “Fokker-action” approach, can be resolved by implementing the so-called zero-bin subtraction in the EFT framework. The procedure yields ambiguity-free results without the need of additional information beyond the PN expansion.

We analyze the behavior of causal geodesics on a Kerr-de Sitter spacetime with particular emphasis on their completeness property. We set up an initial value problem of which the solutions lead to a global understanding of causal geodesics on these spacetimes. Causal geodesics that avoid the rotation axis are complete except the ones that hit the ringlike curvature singularity and those that encounter the ring singularity are necessary equatorial ones. We also show the existence of geodesics that cross or lie on the rotation axis. The equations governing the latter family show the repulsive nature of the ring singularity. The results of this work show that, as far as properties of causal geodesics are concerned, Kerr-de Sitter spacetimes behave in a similar manner as the family of Kerr spacetimes.

The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behavior of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the Stückelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameter space identified by requiring no-ghost instabilities and positive squared speeds of propagation does not change by performing a field redefinition, while the requirement of the avoidance of tachyonic instability might instead be different. Therefore, we find it interesting to associate to the general modified gravity theory described in the effective field theory framework, a perturbation field which will inherit all of the properties of the theory. In the present paper we address the following questions: (1) how can we define such a field? and (2) what is the mass of such a field as the background approaches a final de Sitter state? We define a gauge-invariant quantity which identifies the density of the dark energy perturbation field valid for any background. We derive the mass associated to the gauge-invariant dark energy field on a de Sitter background, which we retain to be still a good approximation also at very low redshift ($z\simeq 0$). On this background we also investigate the value of the speed of propagation and we find that there exist classes of theories which admit a nonvanishing speed of propagation, even in the Horndeski model, for which a zero speed of sound has previously been found in the literature. We finally apply our results to specific well-known models.

We examine potential deformations of inner black hole and cosmological horizons in Reissner-Nordström de Sitter spacetimes. While the rigidity of the outer black hole horizon is guaranteed by theorem, that theorem applies to neither the inner black hole nor the past cosmological horizon. Further, for pure de Sitter spacetime, it is clear that the cosmological horizon can be deformed (by translation). For specific parameter choices, it is shown that both inner black hole and cosmological horizons can be infinitesimally deformed. However, these do not extend to finite deformations. The corresponding results for general spherically symmetric spacetimes are considered.

A generic, noneccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by seven intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einstein’s equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all seven dimensions of the intrinsic noneccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of 744 numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to 0.8 and mass ratios up to 2, includes all $\ell \le 4$ modes, begins about 20 orbits before merger, and can be evaluated in $\sim 50\mathrm{ms}$. We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that were not previously possible when using highly accurate waveforms, such as parameter inference and tests of general relativity with GW observations.

Extending the Proca Lagrangian of a massive complex-valued vector field by self-interaction potential, we construct a large class of spherically symmetric solutions in flat Minkowski background as well as in the self-gravitating case. Our solutions encompass Proca $Q$ balls and Proca stars known in the literature, but present new features and go beyond the limited region of parameter space charted so far. A special emphasis is set on the domain of existence of the solutions in relation with the coupling constants of the potential and to the critical phenomena limiting this domain.

We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in the redshift range $0\le z\le 0.8$, after applying a conservative 80% mass scatter prior on each cluster and marginalizing over all other parameters, we forecast $1\sigma$ constraints on the dark energy equation of state $w$ and matter density parameter ${\mathrm{\Omega }}_M$ of ${\sigma }_w=0.138(0.431)$ and ${\sigma }_{{\mathrm{\Omega }}_M}=0.007(0.025)$ in a flat universe. Assuming 40% mass scatter and adding a prior on the Hubble constant we can achieve a constraint on the Chevallier-Polarski-Linder parametrization of the dark energy equation of state parameters $w_0$ and $w_a$ with 100 clusters in the same redshift range: ${\sigma }_{w_0}=0.191$ and ${\sigma }_{w_a}=2.712$. Dropping the assumption of flatness and assuming $w=-1$ we also attain competitive constraints on the matter and dark energy density parameters: ${\sigma }_{{\mathrm{\Omega }}_M}=0.101$ and ${\sigma }_{{\mathrm{\Omega }}_{\mathrm{\Lambda }}}=0.197$ for 100 clusters uniformly distributed in the range $0\le z\le 0.8$ after applying a prior on the Hubble constant. We also discuss various observational strategies for tightening constraints in both the near and far future.

We construct an updated and extended compilation of growth-rate data based on recent redshift-space distortion measurements. The data set consists of 34 data points and includes corrections for model dependence. In order to minimize overlap and maximize the independence of the data points, we also construct a subsample of this compilation (a “gold” growth data set) which consists of 18 data points. We test the consistency of this data set with the best-fit $\mathrm{Planck}15/\mathrm{\Lambda }\mathrm{CDM}$ parameters in the context of General Relativity using the evolution equation for the growth factor $\delta (a)$ with a $w\mathrm{CDM}$ background. We find tension at the $\sim 3\sigma$ level between the best-fit parameters $w$ (the dark energy equation of state), ${\mathrm{\Omega }}_{0m}$ (the matter density parameter), and ${\sigma }_8$ (the matter power spectrum normalization on scales $8h^{-1}\mathrm{Mpc}$) and the corresponding $\mathrm{Planck}15/\mathrm{\Lambda }\mathrm{CDM}$ parameters ($w=-1$, ${\mathrm{\Omega }}_{0m}=0.315$, and ${\sigma }_8=0.831$). We show that the tension disappears if we allow for evolution of the effective Newton constant, parametrized as $G_{\mathrm{eff}}(a)/G_{\mathrm{N}}=1+g_a(1-a{)}^n-g_a(1-a{)}^{2n}$ with $n\ge 2$ where $g_a$ and $n$ are parameters of the model, $a$ is the scale factor, and $z=1/a-1$ is the redshift. This parametrization satisfies three important criteria: a) positive energy of the graviton ($G_{\mathrm{eff}}>0$), b) consistency with big bang nucleosynthesis constraints ($G_{\mathrm{eff}}(a\ll 1)/G_{\mathrm{N}}=1$), and c) consistency with Solar System tests ($G_{\mathrm{eff}}(a=1)/G_{\mathrm{N}}=1$ and $G_{\mathrm{eff}}^{\prime }(a=1)/G_{\mathrm{N}}=0$). We show that the best-fit form of $G_{\mathrm{eff}}(z)$ obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of $z$), and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best-fit $G_{\mathrm{eff}}(z)$ obtained from the Planck cosmic microwave background power spectrum on large angular scales and show that it is a mildly increasing function of $z$, in $3\sigma$ tension with the corresponding decreasing best-fit $G_{\mathrm{eff}}(z)$ obtained from the growth data.

Cosmic inflation, a period of accelerated expansion in the early universe, can give rise to large amplitude ultralarge scale inhomogeneities on distance scales comparable to or larger than the observable universe. The cosmic microwave background (CMB) anisotropy on the largest angular scales is sensitive to such inhomogeneities and can be used to constrain the presence of ultralarge scale structure (ULSS). We numerically evolve nonlinear inhomogeneities present at the beginning of inflation in full general relativity to assess the CMB quadrupole constraint on the amplitude of the initial fluctuations and the size of the observable universe relative to a length scale characterizing the ULSS. To obtain a statistically meaningful ensemble of simulations, we adopt a toy model in which inhomogeneities are injected along a preferred direction. We compute the likelihood function for the CMB quadrupole including both ULSS and the standard quantum fluctuations produced during inflation. We compute the posterior given the observed CMB quadrupole, finding that when including gravitational nonlinearities, ULSS curvature perturbations of order unity are allowed by the data, even on length scales not too much larger than the size of the observable universe. To demonstrate the robustness of our conclusions, we also explore a semianalytic model for the ULSS which reproduces our numerical results for the case of planar symmetry, and which can be extended to ULSS with a three-dimensional inhomogeneity structure. Our results illustrate the utility and importance of numerical relativity for constraining early universe cosmology.

The contribution of one-loop millicharged fermion vacuum polarization in a cosmic magnetic field to the cosmic microwave background (CMB) polarization is considered. Exact and perturbative solutions of the density matrix equations of motion in terms of the Stokes parameters are presented. For linearly polarized CMB at the decoupling time, it is shown that the propagation of CMB photons in a cosmic magnetic field would generate elliptic polarization (circular and linear) of the CMB due to millicharged fermion vacuum polarization. Analytic expressions for the degree of circular polarization and rotation angle of the polarization plane of the CMB are presented. Depending on the ratio of millicharged fermion relative charge to mass, $\epsilon /m_{\epsilon }$, magnetic field amplitude, and CMB observation frequency, it is shown that the acquired CMB degree of circular polarization could be of the order of magnitude $P_C(T_0)\sim {10}^{-10}–{10}^{-6}$ in the best scenario for a canonical value of magnetic field amplitude of the order of $\sim \mathrm{nG}$ and $\epsilon /m_{\epsilon }\sim {10}^{-4}–\mathrm{few}\times {10}^{-3}$. The mechanism considered in this work generates CMB polarization even in the case when the CMB is initially in thermal equilibrium. Limits on the magnetic field amplitude due to prior-decoupling CMB polarization are presented.

The destabilizing role of neutrino beams on the Trivelpiece-Gould modes is considered, assuming electrostatic perturbations in a magnetized plasma composed by electrons in a neutralizing ionic background, coupled to a neutrino species by means of an effective neutrino force arising from the electroweak interaction. The magnetic field is found to significantly improve the linear instability growth rate, as calculated for supernova type II environments. On the formal level, for wave vectors parallel or perpendicular to the magnetic field, the instability growth rate is found from the unmagnetized case replacing the plasma frequency by the appropriated Trivelpiece-Gould frequency. The growth rate associated with oblique propagation is also obtained.

We analyze the secular evolution of hierarchical triple systems in the post-Newtonian approximation to general relativity. We expand the Newtonian three-body equations of motion in powers of the ratio $a/A$, where $a$ and $A$ are the semimajor axis of the inner binary’s orbit and of the orbit of the third body relative to the center of mass of the inner binary, respectively. The leading order “quadrupole” terms, of order $(a/A{)}^3$ relative to the $1/a^2$ acceleration within the inner binary, are responsible for the well-known Kozai-Lidov oscillations of orbital inclination and eccentricity. The octupole terms, of order $(a/A{)}^4$ have been shown to allow the inner orbit to “flip” from prograde relative to the outer orbit to retrograde and back, and to permit excursions to very large eccentricities. We carry the expansion of the equations of motion to hexadecapole order, corresponding to contributions of order $(a/A{)}^5$. We also include the leading orbital effects of post-Newtonian theory, namely the pericenter precessions of the inner and outer orbits. Using the Lagrange planetary equations for the orbit elements of both binaries, we average over orbital time scales, obtain the equations for the secular evolution of the elements through hexadecapole order, and employ them to analyze cases of astrophysical interest. We find that, for the most part, the orbital flips found at octupole order are robust against both relativistic and hexadecapole perturbations. We show that, for equal-mass inner binaries, where the octupole terms vanish, the hexadecapole contributions can alone generate orbital flips and excursions to very large eccentricities.

We study the scalar singlet as well as the two-Higgs doublet model inert dark matter particles’ impact on compact objects, and we provide the first constraints of the parameter space using neutron stars. The models discussed here are characterized by two free parameters, namely the mass $M_{\chi }$ of the scalar particle that plays the role of the dark matter in the Universe, and a dimensionless coupling constant ${\lambda }_{\chi }$ that determines the strength of the interaction of the dark matter particles with the Standard Model Higgs boson. By considering a typical neutron star we are able to obtain constraints on scalar dark matter depending on the dark matter (DM) annihilation cross section and self-interaction coupling constant. Our findings show that (i) for heavy DM particles neutron stars can provide us with bounds better that the current limits from direct detection searches only when the self-annihilations of DM particles are negligible and the DM self-interaction coupling constant is very small, while (ii) for light DM particles the bounds obtained here are comparable to limits from Higgs invisible decays unless the DM particles are extremely light.

The Sun is a bright source of GeV gamma rays, due to cosmic rays interacting with solar matter and photons. Key aspects of the underlying processes remain mysterious. The emission in the TeV range, for which there are neither observational nor theoretical studies, could provide crucial clues. The new experiments HAWC (running) and LHAASO (planned) can look at the Sun with unprecedented sensitivity. In this paper, we predict the very high-energy (up to 1000 TeV) gamma-ray flux from the solar disk and halo, due to cosmic-ray hadrons and electrons ($e^{+}+e^{-}$), respectively. We neglect solar magnetic effects, which is valid at TeV energies; at lower energies, this gives a theoretical lower bound on the disk flux and a theoretical upper bound on the halo flux. We show that the solar-halo gamma-ray flux allows the first test of the $\sim 5–70\mathrm{TeV}$ cosmic-ray electron spectrum. Further, we show that HAWC can immediately make an even stronger test with nondirectional observations of cosmic-ray electrons. Together, these gamma-ray and electron studies will provide new insights about the local density of cosmic rays and their interactions with the Sun and its magnetic environment. These studies will also be an important input to tests of new physics, including dark matter.

One of the simplest extensions of the Standard Model is the inclusion of an additional scalar multiplet, and we consider scalars in the $SU(2{)}_L$ singlet, triplet, and quartet representations. We examine models with heavy neutral scalars, $m_H\sim 1–2\mathrm{TeV}$, and the matching of the UV complete theories to the low energy effective field theory. We demonstrate the agreement of the kinematic distributions obtained in the singlet models for the gluon fusion of a Higgs pair with the predictions of the effective field theory. The restrictions on the extended scalar sectors due to unitarity and precision electroweak measurements are summarized and lead to highly restricted regions of viable parameter space for the triplet and quartet models.

We present a full one-loop renormalization of the Higgs sector of the next-to-minimal-supersymmetric-Standard-Model (NMSSM) and its implementation within sloops, a code for the automated computations of one-loop processes in theories beyond the Standard Model. The present work is the sequel to the study we performed on the renormalization of the sectors of the NMSSM comprising neutralinos, charginos, and sfermions, thereby completing the full one-loop renormalization of the NMSSM. We have investigated several renormalization schemes based on alternative choices (on-shell or $\overline{\mathrm{DR}}$) of the physical parameters. Special attention is paid to the issue of the mixing between physical fields. To weigh the impact of the different renormalization schemes, the partial widths for the decays of the Higgs bosons into supersymmetric particles are computed at one loop. In many decays large differences between the schemes are found. We discuss the origin of these differences. In particular, we study two contrasting scenarios. The first model is MSSM-like with a small value for the mixing between the doublet and singlet Higgs superfields while the second model has a moderate value for this mixing. We critically discuss the issue of the reconstruction of the underlying parameters and their counterterms in the case of a theory with a large number of parameters, such as the NMSSM, from a set of physical parameters. In the present study this set corresponds to the minimum set of masses for the implementation of the on-shell schemes.

In this paper, we present a calculation of the $\gamma +j$ process at next-to-next-to-leading order (NNLO) in QCD and compare the resulting predictions to 8 TeV CMS data. We find good agreement with the shape of the photon $p_T$ spectrum, particularly after the inclusion of additional electroweak corrections, but there is a tension between the overall normalization of the theoretical prediction and the measurement. We use our results to compute the ratio of $Z(\to {\ell }^{+}{\ell }^{-})+j$ to $\gamma +j$ events as a function of the vector boson transverse momentum at NNLO, a quantity that is used to normalize $Z(\to \nu \overline{\nu })+j$ backgrounds in searches for dark matter and supersymmetry. Our NNLO calculation significantly reduces the theoretical uncertainty on this ratio, thus boosting its power for future searches of new physics.

The structure of $d^{*}(2380)$ is restudied with the single cluster structure in the chiral SU(3) quark model which has successfully been employed to explain the $N-N$ scattering data and the binding energy of deuteron. The binding behavior of such a six quark system is solved by using a variational method. The trial wave function is chosen to be a combination of a basic spherical symmetric component of $[(0s{)}^6{]}_{\mathrm{orb}}$ in the orbital space with $0\hslash \omega$ excitation and an inner structural deformation component of $[(0s{)}^5(1s){]}_{\mathrm{orb}}$ and $[(0s{)}^4(0p{)}^2{]}_{\mathrm{orb}}$ in the orbital space with $2\hslash \omega$ excitation, both of which are in the spatial $[6{]}_{\mathrm{orb}}$ symmetry. It is shown that the mass of the system is about 2356 MeV, which is qualitatively consistent with the result both from the two-cluster configuration calculation and from the data measured by the WASA Collaborations. When the meson exchange interactions are absent, the attraction is insufficient to form a stable state below the $\mathrm{\Delta }\mathrm{\Delta }$ threshold. This result tells us that as long as the medium-range interaction due to the chiral symmetry consideration is properly introduced, the mass of the system will be reduced in a rather large extent. It also implies that the observed $d^{*}$ is a six-quark bound state with respect to the $\mathrm{\Delta }\mathrm{\Delta }$ threshold, which again supports the conclusion that $d^{*}$ is a hexaquark dominant state.

We study the final-state-interaction contributions to the transitions from the $Z_b(10610)$ and $Z_b(10650)$ to $S$-wave bottomonium via $\pi$, $\rho$, and photon emission. Our estimations indicate that the final-state interaction plays important roles in the hidden bottom decays of $Z_b(10610)$ and $Z_b(10650)$. With this mechanism, the branching ratios of the observed $\mathrm{\Upsilon }(nS)\pi (n=1,2,3)$ channels could be reproduced and the branching ratios of $Z_b(10610)/Z_b(10650)\to {\eta }_b(mS)\rho /\gamma (m=1,2)$ are predicted, which could be further tested at Belle II in the near future.

In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo-based QCD sum rules, which combines the rigorous Hölder-inequality-determined sum rule window and a parametrization with two-Breit-Wigner-type resonances for the phenomenological spectral density that satisfies the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances $\sigma$ and $f_0(980)$, we obtain a prediction for light quark mass $m_q(2\mathrm{GeV})=\frac{1}{2}(m_u(2\mathrm{GeV})+m_d(2\mathrm{GeV}))={4.7}_{-0.7}^{+0.8}\mathrm{MeV}$, which is consistent with the Particle Data Group value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of $\sigma$ and $f_0(980)$ at 2 GeV, which are approximately 0.64–0.83 and 0.40–0.48 GeV, respectively.